Capacitors
()
d
it
C
vt
dt
=
and
() ()
0
11
0
tt
i
d
v
i
d
CC
τ
ττ
−∞
==
+
∫∫
These equations describe an voltage and current that adhere to the passive convention.
All of the currents and voltages are constant in a dc circuit. When the capacitor voltage is
constant, the capacitor current is zero.
Capacitors act like open circuits in dc circuits.
Suppose the capacitor voltage is discontinuous, for example
4.3
2.5
4.4
2.5
t
t
<
⎧
=
⎨
>
⎩
That is, the voltage changes from 4.3 V to 4.4 V abruptly at time
2.5 s
t
=
. At
, the
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 Spring '08
 gong
 Calculus, Volt, Electric charge, Continuous function, Voltage drop

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